Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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      (d)

      2 Find the answers to the following subtraction problems:

      (a)

      (b)

      (c)

      (d)

Sign-Switching: Understanding Negation and Absolute Value

       When you attach a negative sign to any number, you negate that number. Negating a number means changing its sign to the opposite sign, so

       Attaching a negative sign to a positive number makes it negative.

       Attaching a negative sign to a negative number makes it positive. The two adjacent (side-by-side) negative signs cancel each other out.

       Attaching a negative sign to 0 doesn’t change its value, so .

      In contrast to negation, placing two bars around a number gives you the absolute value of that number. Absolute value is the number’s distance from 0 on the number line — that is, it’s the positive value of a number, regardless of whether you started out with a negative or positive number:

       The absolute value of a positive number is the same number.

       The absolute value of a negative number makes it a positive number.

       Placing absolute value bars around 0 doesn’t change its value, so .

       Placing a negative sign outside absolute value bars gives you a negative result — for example, .

      Q. Negate the number 7.

      A. −7. Negate 7 by attaching a negative sign to it: −7.

      Q. Find the negation of −3.

      A. 3. The negation of . The two adjacent negative signs cancel out, which gives you 3.

      Q. What’s the negation of ?

      A. 5. First, do the subtraction, which tells you . To find the negation of −5, attach a negative sign to the answer: . The two adjacent negative signs cancel out, which gives you 5.

      Q. What number does equal?

      A. 9. The number 9 is already positive, so the absolute value of 9 is also 9.

      Q. What number does equal?

      A. 17. Because −17 is negative, the absolute value of .

      Q. Solve this absolute value problem:

      A. −4. Do the subtraction first: , which is negative, so the absolute value of . But the negative sign on the left (outside the absolute value bars in the original expression) negates this result, so the answer is −4.

      3 Negate each of the following numbers and expressions by attaching a negative sign and then canceling out negative signs when possible:

      (a)

      (b)

      (c)

      (d)

      (e)

      (f)

      4 Solve the following absolute value problems:

      (a)

      (b)

      (c)

      (d)

      (e)

(f)

Addition and Subtraction with Negative Numbers

      The great secret to adding and subtracting negative numbers is to turn every problem into a series of ups and downs on the number line. When you know how to do this, you find that all these problems are quite simple.

      So in this section,

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